The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A188392 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
newer changes | Showing entries 11-20

A188392

T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column.
(history; published version)

#10 by Andrew Howroyd at Mon Dec 10 16:16:20 EST 2018

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

T(n, k)={my(s=0); forpart(p=n*k, s+=permcount(p)*polcoef(prod(i=1, #p, 1 + x^p[i] + O(x*x^n)), n)^k); s/(n*k)!} \\ Andrew Howroyd, Dec 10 2018

#9 by Andrew Howroyd at Mon Dec 10 16:10:36 EST 2018

EXAMPLE

Table startsArray begins:

========================================================================

n\k| 1 2 3 4 5 6 7 8

---+--------------------------------------------------------------------

.1.. | 1 2... 5..... 15........ 52.......... 203........... 877........... 4140

.2 | 1.. 3.. 16.... 139...... 1750........ 29388........ 624889....... 16255738

.3 | 1.. 4.. 39.... 862..... 35775...... 2406208..... 238773109.... 32867762616

.4 | 1.. 5.. 81... 4079.... 507549.... 127126912... 55643064708. 38715666455777

.5 | 1.. 6. 150.. 15791... 5442547... 4762077620. 8738543204786

.6 | 1.. 7. 256.. 52450.. 46757209. 135029200594

.7 | 1.. 8. 410. 154279. 335279744

.8 | 1.. 9. 625. 411180

.9 | 1. 10. 915

.1.11

...

All solutions for 6X26 X 2

#8 by Andrew Howroyd at Mon Dec 10 15:31:53 EST 2018

COMMENTS

Table starts

.1..2...5.....15........52..........203...........877...........4140

.1..3..16....139......1750........29388........624889.......16255738

.1..4..39....862.....35775......2406208.....238773109....32867762616

.1..5..81...4079....507549....127126912...55643064708.38715666455777

.1..6.150..15791...5442547...4762077620.8738543204786

.1..7.256..52450..46757209.135029200594

.1..8.410.154279.335279744

.1..9.625.411180

.1.10.915

.1.11

EXAMPLE

Table starts:

.1..2...5.....15........52..........203...........877...........4140

.1..3..16....139......1750........29388........624889.......16255738

.1..4..39....862.....35775......2406208.....238773109....32867762616

.1..5..81...4079....507549....127126912...55643064708.38715666455777

.1..6.150..15791...5442547...4762077620.8738543204786

.1..7.256..52450..46757209.135029200594

.1..8.410.154279.335279744

.1..9.625.411180

.1.10.915

.1.11

...

CROSSREFS

Rows 1..6 are A000110, A020554, A165434, A165435, A165436, A165437.

Row 1 is A000110.

Row 2 is A020554.

Row 3 is A165434.

Row 4 is A165435.

Row 5 is A165436.

Row 6 is A165437.

STATUS

approved

editing

#7 by Alois P. Heinz at Sun Oct 18 11:20:00 EDT 2015

STATUS

editing

approved

#6 by Alois P. Heinz at Sun Oct 18 11:19:56 EDT 2015

NAME

T(n,k) =Number number of (n*k)Xk X k binary arrays with rows in nonincreasing order and n ones in every column.

CROSSREFS

Column 3 is A011863(n+1).

Column 4 is A175707.

Row 1 is A000110.

Row 2 is A020554.

Row 3 is A165434.

Row 4 is A165435.

Row 5 is A165436.

Row 6 is A165437.

AUTHOR

R. H. Hardin , Mar 30 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:12 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Mar 30 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Wed Mar 30 10:00:28 EDT 2011

STATUS

proposed

approved

#3 by Ron Hardin at Wed Mar 30 10:00:18 EDT 2011

LINKS

R. H. Hardin, <a href="/A188392/b188392.txt">Table of n, a(n) for n = 1..69</a>

#2 by Ron Hardin at Wed Mar 30 09:59:48 EDT 2011

NAME

allocated for Ron HardinT(n,k)=Number of (n*k)Xk binary arrays with rows in nonincreasing order and n ones in every column

DATA

1, 2, 1, 5, 3, 1, 15, 16, 4, 1, 52, 139, 39, 5, 1, 203, 1750, 862, 81, 6, 1, 877, 29388, 35775, 4079, 150, 7, 1, 4140, 624889, 2406208, 507549, 15791, 256, 8, 1, 21147, 16255738, 238773109, 127126912, 5442547, 52450, 410, 9, 1, 115975, 504717929, 32867762616

OFFSET

1,2

COMMENTS

Table starts

.1..2...5.....15........52..........203...........877...........4140

.1..3..16....139......1750........29388........624889.......16255738

.1..4..39....862.....35775......2406208.....238773109....32867762616

.1..5..81...4079....507549....127126912...55643064708.38715666455777

.1..6.150..15791...5442547...4762077620.8738543204786

.1..7.256..52450..46757209.135029200594

.1..8.410.154279.335279744

.1..9.625.411180

.1.10.915

.1.11

EXAMPLE

All solutions for 6X2

..1..1....1..1....1..0....1..1

..1..1....1..1....1..0....1..0

..1..0....1..1....1..0....1..0

..0..1....0..0....0..1....0..1

..0..0....0..0....0..1....0..1

..0..0....0..0....0..1....0..0

CROSSREFS

Column 3 is A011863(n+1)

Column 4 is A175707

Row 1 is A000110

Row 2 is A020554

Row 3 is A165434

Row 4 is A165435

Row 5 is A165436

Row 6 is A165437

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Mar 30 2011

STATUS

approved

proposed

#1 by Ron Hardin at Wed Mar 30 09:51:52 EDT 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved